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The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
The evolutional scenario of the resource distribution in the fractal-cluster systems which is identified as an "organism" has been suggested. We propose a model in which the resource redistribution dynamics in the closed system is…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
A first step in exploring population structure in crop plants and other organisms is to define the number of subpopulations that exist for a given data set. The genetic marker data sets being generated have become increasingly large over…
Crystal structure generation is a foundational challenge in materials discovery, particularly in designing functional inorganic crystalline materials with desired properties. Most existing diffusion-based generative models for crystals rely…
Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…
We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
In order to understand the Galactic structure, we perform a statistical analysis of the distribution of various cluster parameters based on an almost complete sample of Galactic open clusters yet available. The geometrical and physical…
Molecules reside broadly in the interstellar space and can be detected via spectroscopic observations. To date, more than 271 molecular species have been identified in interstellar medium or circumstellar envelopes. Molecular spectroscopic…
Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be…
Good statistics for measuring large-scale structure in the Universe must be able to distinguish between different models of structure formation. In this paper, two and three dimensional ``counts in cell" statistics and a new ``discrete…
Evolution of the statistical distribution of density field is investigated by means of a counts-in-cells method in a low-density cold-dark-matter simulated universe. Four theoretical distributions, i.e. the negative binomial distribution,…
As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a…
Star clusters are ideal tracers of star formation activity in systems outside the volume that can be studied using individual, resolved stars. These unresolved clusters span orders of magnitude in brightness and mass, and their formation is…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
A statistical model for the calculation of the ionisation-cluster size distribution in nanodosimetry is proposed. It is based on a canonical ensemble and derives from the well-known nuclear droplet model. The model especially can be applied…
Determining whether a candidate crystalline material is thermodynamically stable depends on identifying its true ground-state structure, a central challenge in computational materials science. We introduce CrystalGRW, a diffusion-based…
The traditional method of morphological classification, by visual inspection of images of uniform quality and by reference to standards for each type, is critically examined. The rate of agreement among traditional morphologists on the…
The numbers of natural chemical elements, minerals, inorganic and organic chemical compounds are determined by 1, 2, 3 and 4-combinations of a set 95 and are respectively equal to 95, 4,465, 138,415 and 3,183,545. To explain these relations…